In multi-transmitter wireless communications systems, channel access techniques allow multiple transmitters connected to the same physical channel to share its transmission capacity. Various channel access techniques are known in the art. In second generation communications systems according to the Global System for Mobile communications (GSM) standard, Time Division Multiple Access (TDMA) techniques are utilized to divide a specific frequency channel into individual time slots which are then assigned to individual transmitters. In third generation communications systems, Code Division Multiple Access (CDMA) techniques divide channel access in the signal space by employing a combination of spread spectrum operations and a special coding scheme in which each transmitter is assigned an individual code. The next advance in wireless communications systems considers Orthogonal Frequency Division Multiple Access (OFDMA) techniques to achieve still higher bit rates.
One major advantage of OFDMA over other channel access techniques is its robustness in the presence of multi-path signal propagation. On the other hand, the waveform of OFDMA signals exhibits very pronounced envelope fluctuations resulting in a high Peak-to-Average Power Ratio (PAPR). Signals with high PAPR require highly linear power amplifiers to avoid excessive inter-modulation distortion, and these power amplifiers have to be operated with a large back-off from their peak power. The result is a low power efficiency, which places a significant burden on battery operated transmitters such as mobile telephones.
The disadvantage of a high PAPR is overcome by SC-FDMA, which can be regarded as a modification of OFDMA. For this reason, the Third Generation Partnership Project (3GPP) is considering using SC-FDMA in fourth generation communications systems for the uplink direction towards the access network. In context with the Long Term Evolution (LTE) project of 3GPP, the Technical Specification TS 36.211 V8.0.0 ‘Physical Channels and Modulation’, September 2007, specifies the time-continuous SC-FDMA signal sl(t) as (using the notation defined in TS 36.211 hereinafter):
                    s        l            ⁡              (        t        )              =                  ∑                  k          =                      -                          ⌊                                                N                  RB                  UL                                ⁢                                                      N                    sc                    RB                                    /                  2                                            ⌋                                                            ⌈                                          N                RB                UL                            ⁢                                                N                  sc                  RB                                /                2                                      ⌉                    -          1                    ⁢                                    a                                          k                                  (                  -                  )                                            ,              l                                ·                      ⅇ                          j2              ⁢                                                          ⁢                              π                ⁡                                  (                                      k                    +                                          1                      /                      2                                                        )                                            ⁢              Δ              ⁢                                                          ⁢                              f                ⁡                                  (                                      t                    -                                                                  N                                                  CP                          ,                          l                                                                    ⁢                                              T                        s                                                                              )                                                                    ⁢                                  ⁢        for                  0    ≤    t    <                  (                              N                          CP              ,              l                                +          N                )            ⁢                        T          s                .            
With sub-carrier spacing Δƒ=1/(NTs), and with the number of orthogonal sub-carriers in one half of the available uplink spectrumB=NRBULNscRB/2,which—with the possible parameter values specified in TS 36.211—is guaranteed to be integer, the following expression for symbols of the time-continuous SC-FDMA signal can be obtained:
            s      l        ⁡          (              nT        s            )        =                    ∑                  k          =                      -            B                                    B          -          1                    ⁢                                    a                                          k                                  (                  -                  )                                            ,              l                                ·                      ⅇ                          j              ⁢                                                          ⁢              2              ⁢                              π                ⁡                                  (                                      k                    +                                          1                      /                      2                                                        )                                            ⁢                                                (                                      n                    -                                          N                                              CP                        ,                        l                                                                              )                                /                N                                                    ⁢                                  ⁢        for        ⁢                                  ⁢        0              ≤    n    <                  (                              N                          CP              ,              l                                +          N                )            .      
The frequency-domain index of a resource element (RE) isk(−)=k+B with 0≦k(−)<2B. 
The modulation symbols to be mapped on resource elements are specified—for SC-FDMA symbol l=0, which does not restrict the generality—as:
      z    ⁡          (              k        DFT            )        =                    ∑                  i          =          0                                      M            sc            PUSCH                    -          1                    ⁢                                    d            ⁡                          (              i              )                                ·                      ⅇ                                          -                j2                            ⁢                                                          ⁢              π              ⁢                                                          ⁢                              k                DFT                            ⁢                              i                /                                  M                  sc                  PUSCH                                                                    ⁢                                  ⁢        for        ⁢                                  ⁢        0              ≤          k      DFT        <                  M        sc        PUSCH            .      
The complex-valued symbols from data mapping (baseband modulation) are given by d(i). The mapping of modulation symbols to REs is done such thatk(−)=k0+ƒhop+kDFT=K+kDFT with K=k0+ƒhop.
An exemplary implementation of an SC-FDMA modulator stage is discussed in Myung et al., ‘Single Carrier FDMA for Uplink Wireless Transmission’, IEEE Vehicular Technology Magazine, pp. 30-38, September 2006. Another exemplary realization of an SC-FDMA modulator stage 10 will now be discussed with reference to the schematic illustration in FIG. 1.
The modulator stage 10 receives as input signal a multilevel sequence of complex-valued symbols in one of several possible modulation formats such as Binary Phase Shift Keying (BPSK) or 16 level Quadrature Amplitude Modulation (16-QAM). The modulation symbols are received in sets (also called blocks) containing M symbols each, and every set of M symbols is subjected to an M-point Discrete Fourier Transform (DFT) in a DFT block 12 to obtain a frequency domain representation of the M symbols.
Next, the M DFT outputs are mapped to one of N (N>M) orthogonal sub-carriers in a mapping block 14. In TS 36.211, the value of M is defined to beMscPUSCH=12·2α2·3α3·5α5≦1320.
The mapping block 14 outputs a set of N complex sub-carrier amplitudes, and exactly M of the amplitudes will be non-zero.
The sub-carrier amplitudes output by the mapping block 14 are re-transformed by an Inverse Fast Fourier Transform (IFFT) block 16 to a time domain signal, and the time domain signal is subjected to a phase rotation in a block 18 to correct any phase errors introduced by the previous signal processing operations in blocks 12 to 16. In addition to subjecting the output signal of the IFFT block 16 to a phase rotation, a Cyclic Prefix (CP) is inserted also (not shown in FIG. 1). The CP provides a guard-time between two sequentially transmitted symbol blocks to reduce inter-block interference caused by multi-path propagation.
One drawback of conventional SC-FDMA transmitters is the implementation of the DFT block 12. Let M be the number of input symbols, then the number of multiplications and additions that will have to be performed in the DFT block 12 is in the order of M*M. For this reason, considerable processing power is required to realize the transmitter stage 10, and processing power is a scarce resource especially in battery operated transmitters. To reduce the required processing power, a mixed radix FFT according to the Cooley-Tukey algorithm can be implemented. As is well known, such a mixed radix FFT is most efficient if M is a product of as low as possible prime factors. (And for this reason, TS 36.211 restricts the prime factors of M to 2, 3 and 5 as shown in the above formula.)
The restriction to specific prime factors imposes an undesirable restriction on the possible values of M. Moreover, it has been found that hardware implementations of mixed radix FFTs are often rather complicated.